Answer
(a) Less than
(b) I
Work Step by Step
(a) We know that $v\propto \sqrt{2}$. As the absolute temperature of an ideal gas is doubled from $100K$ to $200K$, hence average speed is increased by a factor $\sqrt{2}=1.414$, which means the average speed is increased by a factor less than $2$.
(b) We know that the best explanation is option (I) -- that is, doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor which is less than 2.
